How would you test to see if the die is fair?

Lets answer one of the questions posed above. Suppose we roll two fair dice. What's the probability that the sum of the upfaces is 7 or 11? Here's the sample space again:

6 - * * * * * * Die 2 - - 5 - * * * * * * + - - 4 - * * * * * * - + 3 - * * * * * * - - 2 - * * * * * * + - 1 - * * * * * * ----+---------+---------+---------+---------+---------+--Die 1 1 2 3 4 5 6

Since the dice are fair, it seems that each of the points is equilikely. Since there are 8 (6 as "7" and 2 as "11") elements in the event of interest, the probability of a "7" or "11" is 8/36.

Note if we assume the equilikely case for assigning probabilities, then the probability of any event is just the number of elements in that event divided by the number of elements in the sample space.

- 1.
- Six cards with the numbers 1 through 6 on them are well shuffled and two cards are dealt (without replacment). Find the probability that the sum of the numbers on the two cards is 7. Note order is not important here. For example, the hand with cards 1,2 in it is the same as the hand with cards 2,1. In the sample space there are 15 elements. List them. Then find the probability that the sum of the numbers on the two cards is 7. Why is your answer different from the craps game answer?